Contents

Science and the Universe

Science is an enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the world. Traditionally we use mathematics to explain the physical world, which means theorems, equations, formulas and calculation. So there is a physical universe, and a mathematical universe, and both can be connected in a meaningful way with each other. Each science has its "own universe" which it tries to describe:

Science

studies worlds made by ..

Physics and Natural Science

..atoms (physical or natural universe)

Biology

..cells

Neuroscience

..neurons

Economics

..markets

Sociology

..humans

Mathematics

..numbers (abstract world of numbers and logic quantities)

Philosophy and Humanities

..words (abstract world of thoughts and ideas)

While the natural sciences consider worlds made by atoms, the humanities, esp. linguistics and philosophy, consider worlds made by words. Psychology is an interesting case somewhere in between culture and nature.

Yet there are some open questions: why are there any theorems at all? Could we use computation instead calculation as well? How can we explain social systems? Social systems are part of the physical world, but their form their own universe which is much harder to explain, because it is very complex. It does not contains spherical objects with identical properties, but individual, unique agents which act in unpredictable ways.

New technology can result in new kinds of models and metaphors. During the course of time, the universe has been is compared with a giant clock, a giant machine, a giant computer..

18th century: clocks (machine), newtonian mechanics

19th century: steam engine (machine), thermodynamics

20th century: computers, electrical mechanics

21th century: ..

The computational universe

New technology and unconventional forms of computation can result in new kinds of science and in new universes as well. Computation has given us access to new models and metaphors, but it also opened up the "computational universe". Stephen Wolfram compares in one of his recent essays named Some Modern Perspectives on the Quest for Ultimate Knowledge the exploration of the physical world with the exploration of the "computational universe":

"We have the whole computational universe to explore--with all possible rules. Including, for example, I believe, the rules for our physical universe. [..] over the course of time we have found ways to use a tremendous diversity, say, of possible materials that we can "mine" from the physical world. To find uses for magnetite, or amber, or liquid crystals, or rare earths, or radioactive materials, or whatever. Well, so it will be with the computational universe. [..] It will be interesting to watch the development of technology--as well as art and civilization in general--and to see how it explores the computational universe of possible programs. I'm sure it'll be not unlike the case of physical materials. There'll be techniques for mining, refining, combining. There'll be "gold rushes" as particular rich veins of programs are found."

Some of the gold nuggets have already been found: for example the classical algorithms in computer science for sorting and searching etc., the basic fractals, L-systems and of course cellular automata. In the area of distributed computing, we have discovered big signs saying "It is impossible to find any nuggets here" (for example the FLP theorem), which is quite disappointing.

A coherent theory of computation for "distributed systems" - or something like the principles of distributed computing - is still missing. Traditional computation is associated with calculation: arithmetic functions, serial algorithms, detailed instructions, and sequential operations. Computation in distributed systems such as Cellular Automata and Agent-Based Systems, where iteration meets interaction, is much more complex. A theory, set of theorems or "calculus" for these systems would be desirable, something beyond the Ashby Theorems. It is unclear what can be computed at all
with these systems (what kind of computation would this be?),
what forms and types exist in general (have we found already the basic types?), and how they are connected.

The Wolfram Atlas of Simple Programs is certainly a first step to explore the computational universe. One of Stephen Wolfram's claims in his controversial book "A New Kind of Science" is that the nature of computation must be explored experimentally.

Wolfram's New Kind of Science

A New Kind of Science is a book by Stephen Wolfram, published in 2002. It contains an empirical and systematic study of computational systems such as cellular automata. Wolfram calls these systems simple programs and argues that the scientific philosophy and methods appropriate for the study of simple programs are relevant to other fields of science.